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            <pre><code>P1089 smrtfun

时间: 1000ms / 空间: 131072KiB / Java类名: Main

描述

现有N个物品，第i个物品有两个属性A_i和B_i。在其中选取若干个物品.

使得sum{A_i + B_i}最大，同时sum{A_i}，sum{B_i}均非负（sum{}表示求和）.

输入格式
    第一行，一个整数，表示物品个数N.
    接下来N行，每行两个整数，表示A_i和B_i.

输出格式
一个整数，表示最大的sum{A_i + B_i}.

测试样例1

输入
5 
-5 7 
8 -6 
6 -3 
2 1 
-8 -5

输出
8

备注
 N &lt;= 100 , |A_i| &lt;= 1000 , |B_i| &lt;= 1000</code></pre>
<p>思路：</p>
<p>dp，当</p>
<p>$$ \sum{A_i}=j $$</p>
<p>用f[i][j]表示</p>
<p>$$ max\sum{B_i} $$</p>
<p>由题可知</p>
<p>$$ \sum{A} $$
$$ \sum{B}$$</p>
<p>这两个都是大于0的</p>
<p>又因为j会小于0，数组下标又不能为负</p>
<p>所以我们对所有的j右移十万位</p>
<p>得出转移方程</p>
<pre class="math"><code>f[i][j]=max(f[i-1][j],f[i-1][j-q[i]]+w[i])</code></pre>
<p>类似于背包（傻逼的一批）</p>
<div class="highlight"><pre><span></span><span class="cp">#include</span><span class="cpf">&lt;cstdio&gt;                                                                      </span><span class="cp"></span>
<span class="cp">#include</span><span class="cpf">&lt;cstring&gt;</span><span class="cp"></span>
<span class="cp">#include</span><span class="cpf">&lt;iostream&gt;</span><span class="cp"></span>
<span class="cp">#include</span><span class="cpf">&lt;algorithm&gt;</span><span class="cp"></span>
<span class="cp">#include</span><span class="cpf">&lt;cmath&gt;</span><span class="cp"></span>
<span class="k">using</span> <span class="k">namespace</span> <span class="n">std</span> <span class="p">;</span>
<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span> <span class="o">&amp;</span><span class="n">x</span><span class="p">){</span>
    <span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">int</span> <span class="n">f</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">char</span> <span class="n">ch</span><span class="o">=</span><span class="n">getchar</span><span class="p">();</span>
    <span class="k">while</span><span class="p">(</span><span class="n">ch</span><span class="o">&lt;</span><span class="sc">&#39;0&#39;</span><span class="o">||</span><span class="n">ch</span><span class="o">&gt;</span><span class="sc">&#39;9&#39;</span><span class="p">){</span><span class="n">f</span><span class="o">|=</span><span class="p">(</span><span class="n">ch</span><span class="o">==</span><span class="sc">&#39;-&#39;</span><span class="p">);</span><span class="n">ch</span><span class="o">=</span><span class="n">getchar</span><span class="p">();}</span>
    <span class="k">while</span><span class="p">(</span><span class="n">ch</span><span class="o">&lt;=</span><span class="sc">&#39;9&#39;</span><span class="o">&amp;&amp;</span><span class="n">ch</span><span class="o">&gt;=</span><span class="sc">&#39;0&#39;</span><span class="p">){</span><span class="n">x</span><span class="o">=</span><span class="p">(</span><span class="n">x</span><span class="o">&lt;&lt;</span><span class="mi">1</span><span class="p">)</span><span class="o">+</span><span class="p">(</span><span class="n">x</span><span class="o">&lt;&lt;</span><span class="mi">3</span><span class="p">)</span><span class="o">+</span><span class="p">(</span><span class="n">ch</span><span class="o">^</span><span class="mi">48</span><span class="p">);</span><span class="n">ch</span><span class="o">=</span><span class="n">getchar</span><span class="p">();}</span>
    <span class="n">x</span><span class="o">=</span><span class="n">f</span><span class="o">?-</span><span class="nl">x</span><span class="p">:</span><span class="n">x</span><span class="p">;</span>
    <span class="k">return</span> <span class="p">;</span>
<span class="p">}</span>
<span class="kt">int</span> <span class="n">f</span><span class="p">[</span><span class="mi">110</span><span class="p">][</span><span class="mi">200010</span><span class="p">];</span>
<span class="kt">int</span> <span class="n">q</span><span class="p">[</span><span class="mi">110</span><span class="p">],</span><span class="n">w</span><span class="p">[</span><span class="mi">110</span><span class="p">];</span>
<span class="kt">int</span> <span class="nf">main</span><span class="p">()</span>
<span class="p">{</span>
    <span class="n">freopen</span><span class="p">(</span><span class="s">&quot;a.in&quot;</span><span class="p">,</span><span class="s">&quot;r&quot;</span><span class="p">,</span><span class="n">stdin</span><span class="p">);</span>
    <span class="kt">int</span> <span class="n">n</span><span class="p">,</span><span class="n">ans</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
    <span class="n">read</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="n">read</span><span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="n">i</span><span class="p">]),</span><span class="n">read</span><span class="p">(</span><span class="n">w</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
    <span class="n">memset</span><span class="p">(</span><span class="n">f</span><span class="p">,</span><span class="o">-</span><span class="mh">0x7f</span><span class="p">,</span><span class="k">sizeof</span><span class="p">(</span><span class="n">f</span><span class="p">));</span>
    <span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">100000</span><span class="p">]</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">200000</span><span class="p">;</span><span class="n">j</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">;</span><span class="n">j</span><span class="o">--</span><span class="p">)</span>
            <span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">],</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="n">q</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">+</span><span class="n">w</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">100000</span><span class="p">;</span><span class="n">j</span><span class="o">&lt;=</span><span class="mi">200000</span><span class="p">;</span><span class="n">j</span><span class="o">++</span><span class="p">)</span>
        <span class="k">if</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">)</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">max</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span><span class="n">f</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="o">+</span><span class="n">j</span><span class="o">-</span><span class="mi">100000</span><span class="p">);</span>
    <span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="n">ans</span><span class="p">);</span>
    <span class="k">return</span> <span class="mi">0</span> <span class="p">;</span>
<span class="p">}</span>
</pre></div>
<p>By:Wahacer</p>
<p>2017年10月8日 1:58</p>


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